{"paper":{"title":"Scattering for the radial focusing INLS equation in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos M. Guzm\\'an, Luiz Gustavo Farah","submitted_at":"2017-03-31T17:14:57Z","abstract_excerpt":"We consider the inhomogeneous nonlinear Schr\\\"odinger equation $$ i u_t +\\Delta u+|x|^{-b}|u|^\\alpha u = 0, $$ where $\\frac{4-2b}{N}<\\alpha<\\frac{4-2b}{N-2}$ (when $N=2$, $\\frac{4-2b}{N}<\\alpha<\\infty$) and $0<b<\\min\\{N/3,1\\}$. For a radial initial data $u_0\\in H^1(\\mathbb{R}^N)$ under a certain smallness condition we prove that the corresponding solution is global and scatters. The smallness condition is related to the ground state solution of $-Q+\\Delta Q+ |x|^{-b}|Q|^{\\alpha}Q=0$ and the critical Sobolev index $s_c=\\frac{N}{2}-\\frac{2-b}{\\alpha}$. This is an extension of the recent work \\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10988","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}